Question

A relation R is defined from a set A={2,3,4,5} to a set B={3,6,7,10} as follows: (x,y)£R emplies / inplied by x relatively prime to y .Express R as a set of ordered pair and determine its domain and range

Answer 1

Answer:

R = { (2 , 3) , (2 , 7) , (3 , 7) , (3 , 10) , (4 , 3) , (4 , 7) }.

The domain of R = { 2 , 3 ,4 }

The range of elements of R = { 3 , 7 , 10 }

Step-by-step explanation:

Since:

The pairs in which x and y are relative primes are following

(2 , 3)

(2 , 7)

(3 , 7)

(3 , 10)

(4 , 3)

(4 , 7)

So  the R : A → B define by

R = { (x , y) such that x ∈ A ∧ y ∈ B ∧ gcd(x , y) = 1 }

contains the following elements

R = { (2 , 3) , (2 , 7) , (3 , 7) , (3 , 10) , (4 , 3) , (4 , 7) }.

The domain of R = set of first elements of order pairs contain in R

The domain of R = { 2 , 3 ,4 }

The range of elements of R = set of first elements of order pairs contain in R

The range of elements of R = { 3 , 7 , 10 }.

Answer 2

Answer:

R = { (2 , 3) , (2 , 7) , (3 , 7) , (3 , 10) , (4 , 3) , (4 , 7) }.

The domain of R = { 2 , 3 ,4 }

The range of elements of R = { 3 , 7 , 10 }

Step-by-step explanation:

Since:

The pairs in which x and y are relative primes are following

(2 , 3)

(2 , 7)

(3 , 7)

(3 , 10)

(4 , 3)

(4 , 7)

So  the R : A → B define by

R = { (x , y) such that x ∈ A ∧ y ∈ B ∧ gcd(x , y) = 1 }

contains the following elements

R = { (2 , 3) , (2 , 7) , (3 , 7) , (3 , 10) , (4 , 3) , (4 , 7) }.

The domain of R = set of first elements of order pairs contain in R

The domain of R = { 2 , 3 ,4 }

The range of elements of R = set of first elements of order pairs contain in R

The range of elements of R = { 3 , 7 , 10 }.

Step-by-step explanation: